Preliminaries.
We represent a 3D object as a textured triangle mesh \(\mathbf {O} \equiv (\mathbf {V}, \mathbf {F}, \mathbf {T})\) , where \(\mathbf {V} \in ^{|\mathbf {v}| \times 3}\)  represents the location of the vertices, \(\mathbf {F}\)  represents the faces that define the fixed connectivity of vertices in the mesh, and \(\mathbf {T}\)  represents the texture map.
An individual mesh is iso-morphic to a 2-pole sphere, and thus we model the deformation \(\Delta \mathbf {V}\)  from the initial sphere template, and then obtain the final vertex positions by \(\mathbf {V} = \mathbf {V}_{sphere} + \Delta \mathbf {V}\) . Previous methods [1]}, [2]}, [3]} mostly regress deformation of individual vertices via a fully connected network (MLP). In contrast, recent studies have found that using a 2D convolutional neural network (CNN) to learn a deformation map in the UV space would benefit from consistent semantics across the entire category [4]}, [5]}.
In addition, the deformation map \(\mathbf {S}\)  and the texture map \(\mathbf {T}\)  are topologically aligned, so both the values can be mapped to the mesh via the same predefined mapping function.
